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Main Authors: Liu, Xu, Culver, Adrian B., Harper, Fenner, Roy, Rahul
Format: Preprint
Published: 2023
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Online Access:https://arxiv.org/abs/2308.02728
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author Liu, Xu
Culver, Adrian B.
Harper, Fenner
Roy, Rahul
author_facet Liu, Xu
Culver, Adrian B.
Harper, Fenner
Roy, Rahul
contents Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify noninteracting unitaries in all dimensions on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence.
format Preprint
id arxiv_https___arxiv_org_abs_2308_02728
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Classification of unitary operators by local generatability
Liu, Xu
Culver, Adrian B.
Harper, Fenner
Roy, Rahul
Mesoscale and Nanoscale Physics
Quantum Gases
Strongly Correlated Electrons
Quantum Physics
Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify noninteracting unitaries in all dimensions on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence.
title Classification of unitary operators by local generatability
topic Mesoscale and Nanoscale Physics
Quantum Gases
Strongly Correlated Electrons
Quantum Physics
url https://arxiv.org/abs/2308.02728